Related papers: Hochschild cohomology commutes with adic completio…

For any dg algebra $A$, not necessarily commutative, and a subset $S$ in $H(A)$, the homology of $A$, we construct its derived localisation $L_S(A)$ together with a map $A\to L_S(A)$, well-defined in the homotopy category of dg algebras,…

We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular, we provide a formula for the cup product which gives the cohomology module an algebra structure and then we describe this…

We introduce a formalism of Hochschild (co)-homology for $\mathcal{D}$-cap modules on smooth rigid analytic spaces based on the homological tools of Ind-Banach $\mathcal{D}$-cap modules. We introduce several categories of $\mathcal{D}$-cap…

We borrow ideas from Grothendieck duality theory to noncommutative algebra, and use them to prove a reduction result for Hochschild cohomology for noncommutative algebras which are finite over their center. This generalizes a result over…

Let $A_n$ be the $n$-th Weyl algebra, and let $G\subset\Sp_{2n}(\C)\subset\Aut(A_n)$ be a finite group of linear automorphisms of $A_n$. In this paper we compute the multiplicative structure on the Hochschild cohomology $\HH^*(A_n^G)$ of…

We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give a canonical identification between the usual…

In this paper, we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras. We show that the notion of local cohomology functor can be used to detect the Gorensteinness of a homologically smooth…

Making the first steps towards a classification of simple partial comodules, we give a general construction for partial comodules of a Hopf algebra \(H\) using central idempotents in right coideal subalgebras and show that any…

We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.

Let $G$ be the linear algebraic group $SL_3$ over a field $k$ of characteristic two. Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts rationally by $k$-algebra automorphisms. We show that the full cohomology ring…

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.

It is a well-known result that, in projective space over a field, every set-theoretical complete intersection of positive dimension in connected in codimension one (Hartshorne [H1,3.4.6] or [H2, Theorem 1.3]). Another important…

Let L be a p-adic local field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) is a stably flat completion of its universal enveloping algebra. As a consequence the relative cohomology for the…

Let $R$ be a noetherian commutative ring, and \[ \mathbb F: ...\rightarrow F_2\rightarrow F_1\rightarrow F_0\rightarrow 0 \] a complex of flat $R$-modules. We prove that if $\kappa(\mathfrak p)\otimes_R\mathbb F$ is acyclic for every…

We review results on the first Hochschild cohomology vector space of a finite dimensional algebra, in particular for path algebras modulo a "pre-generated" ideal. In case of a monomial algebra whose quiver has no oriented cycles, a…

Let $R$ be a commutative Noetherian ring and $\mathfrak{a}$ be an ideal of $R$. Suppose $M$ is a finitely generated $R$-module and $N$ is an Artinian $R$-module. We define the concept of filter coregular sequence to determine the infimum of…

Inspired by a question raised by Eisenbud-Musta\c{t}\u{a}-Stillman regarding the injectivity of maps from ${\rm Ext}$ modules to local cohomology modules and the work by the third author with Pham, we introduce a class of rings which we…

Let $R$ denote a commutative Noetherian (not necessarily local) ring, $M$ an arbitrary $R$-module and $I$ an ideal of $R$ of dimension one. It is shown that the $R$-module $\Ext^i_R(R/I,M)$ is finitely generated (resp. weakly Laskerian) for…

Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin,…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…